Applying in Thailand (Thai nationals and residents)
Applications are lodged with the Police Clearance Service Centre, Special Branch Bureau. The applicant provides identification, passport, and any supporting documents the Centre lists for the purpose of the request, and fingerprints are taken through the channel the Centre specifies. Forms, required documents, channels and fees are those published by the Centre at the time of lodgement.
Source: https://pcscenter.sb.police.go.th/
Applying from outside Thailand
Applicants abroad usually have fingerprints taken by the local police or at a Royal Thai Embassy or Consulate, then submit the set to the Police Clearance Service Centre through the channel it publishes, either directly or through an authorised representative in Thailand. Confirm the accepted fingerprint form and posting address with the Centre before taking prints.
Source: https://pcscenter.sb.police.go.th/
Foreign nationals who have lived in Thailand
Australian authorities generally expect police certificates from every country where an applicant has lived for a cumulative period specified in their policy. Foreign nationals who have stayed in Thailand can request a Thai certificate from the Police Clearance Service Centre; check the current requirement and the countries involved against Department of Home Affairs guidance for your visa.
Source: https://immi.homeaffairs.gov.au/
Australian police checks (AFP)
An Australian National Police Check is issued by the Australian Federal Police. Where an immigration application requires it, the AFP publishes the correct check type and purpose code to use; selecting the wrong purpose code is a common cause of a certificate being rejected. Apply through the AFP's own service and follow the code stated by the requesting authority.
Source: https://www.afp.gov.au/
Translating the certificate
A Thai certificate lodged with an Australian authority needs a full translation: header, reference number, the body text, every stamp and signature block, and any annotation on the reverse. Names must be spelled exactly as in the passport across the whole document set. Where the authority requires NAATI certification, the translation is delivered as a PDF carrying the translator's NAATI stamp and signature.
Source: https://www.naati.com.au/